Towards Describing Student Learning of Abstract Algebra: Insights into Learners’ Cognitive Processes from an Acceptance Survey

Abstract

In an earlier contribution to Mathematics, we presented a new teaching concept for abstract algebra in secondary school mathematics, and we discussed findings from mathematics education research indicating that our concept could be used as a promising resource to foster students’ algebraic thinking. In accordance with the Design-Based Research framework, the developed teaching concept is now being revised in several iteration steps and optimised towards student learning. This article reports on the results of the formative assessment of our new teaching concept in the laboratory setting with N=9 individual learners leveraging a research method from science education: The acceptance survey. The results of our study indicate that the instructional elements within our new teaching concept were well accepted by the students, but potential learning difficulties were also revealed. On the one hand, we discuss how the insights gained in learners’ cognitive processes when learning about abstract algebra with our new teaching concept can help to refine our teaching–learning sequence in the sense of Design-Based Research. On the other hand, our results may serve as a fruitful starting point for more in-depth theoretical characterization of secondary school students’ learning progression in abstract algebra.

The role of affective learner characteristics for learning about abstract algebra: A multiple linear regression analysis

“…For example, learners have trouble with the newly presented vocabulary of group theory (cf. Veith et al, 2022a), especially composition and operation are potentially confusing terms that were shown to lead to 2 / 10 fundamental misunderstandings.…”

“…Veith & Bitzenbauer, 2020), merging viewpoints from the new math era (i.e., Griesel, 1965;Kirsch, 1965;Steiner, 1966) Wasserman, 2014;Weber & Larsen, 2008), for example Larsen's (2013aLarsen's ( , 2013b) TAAFU materials. It has been subject to both formative (Veith et al, 2022a) and summative evaluation (Veith et al, 2022c). The core idea lies in introducing learners to groups from a geometric perspective by studying the dihedral groups D3 and D4 as well as cyclical groups ℤ 𝑛 .…”

“…In recent years a body of research has emerged, entirely dedicated towards exploring educational aspects of abstract algebra (Wasserman, 2014(Wasserman, , 2016(Wasserman, , 2017(Wasserman, , 2018 and group theory in particular (Melhuish, 2015(Melhuish, , 2019Melhuish & Fagan, 2018;Pramasdyahsari, 2020;Veith & Bitzenbauer, 2022;Veith et al, 2022aVeith et al, , 2022bVeith et al, , 2022c. Even though group theory is mostly taught on university level mathematics, numerous connections to primary and secondary school mathematics have been uncovered (cf.…”

Analisis Faktor Kesulitan Belajar Ipa Siswa Sekolah Menengah Pertama

“…Kesulitan belajar harus segera diatasi. Dalam mengatasi kesulitan belajar harus diidentifikasi terlebih dahulu masalah kesulitan belajar yang paling mempengaruhi siswa, selanjutnya diambil tindakan yang sesuai dengan kebutuhan siswa (Veith et al, 2022).…”

Algebraic Thinking Profile of Junior High School Students with Reflective Cognitive Style in Solving Mathematics Problems

“…Problem-solving plays an important role in the development of algebra as well as being an interesting field to examine thinking and conceptual changes from arithmetic thinking to algebraic thinking [23][24]. Students' algebraic thinking process can be explored of them by using problem-solving [25][26][27]. According to Suharnan's opinion, most problem-solving or concept-formation activities involve the thinking process [28].…”